Sempai

"On" means that you're actually working on the terminal. As in building it, maintaining it, etc. It's clear from the context that in the example cited, it is referring to the initial construction of the terminal.

"In" or "at" doesn't mean you're working on the terminal. It means you're doing some work where you happen to be inside of it. In the case of "at", you could also just be nearby it.

So I disagree with mdchachi. You can't use "in" or "at" instead of "on" because that would change the meaning too much.

Actually that wasn't his question. He asked if they could be used. Not if they were completely interchangeable.

None of them tell you exactly what is going on without additional context.

A universal design committee was set up when work began on the new terminal.
=> implies that some work (construction) is going on at the very beginning of terminal construction. But it could also be the beginning of some stage of construction. For example it could be about beginning work on the interior of the building.A universal design committee was set up when work began in the new terminal.
=> This one clearly implies that the work is happening inside the terminal. It could be work on the terminal itself or it could be work on something else at that location.A universal design committee was set up when work began at the new terminal.
=> This one says that the work location is the terminal. The work could be on the terminal itself. Or it could be on something else. For example, electrical systems inside or outside the terminal.

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